Never heard of that exemption with any of the agencies I've been connected with, but it would cut the costs somewhat. At least up front. Many county/city/state risk management [ read LIABILITY ] departments err on the side of over-caution regarding due diligence in hiring and the threats of "negligent hiring or retention" lawsuits down the road. So chances are that in most places you'll have to jump through the same hoops everyone else does.
Remember the security for military clearance concerns are somewhat different that the concerns of a civilian police agency as far as employee qualifications are concerned.